Abstract. Calculating the windway area
of an organ pallet valve which is necessary to supply a given set of pipes without
robbing is not straightforward. It is important to use the smallest value
possible if pluck is to be minimised, rather than to rely on conservative design
rules which may result in excessive values. Once the necessary value has
been arrived at, the pallet can then be designed using standard long/thin valve
theory. This paper summarises the results of some experimental work in
this area.

Calculating the size of a pallet to supply a given set of pipes can be done
once the pipe dimensions and wind pressure are available, so that the
quantity of wind they will require can be estimated. However, since the pipe
dimensions also dictate the soundboard layout in terms of bar separations etc,
it is perhaps not surprising that the pallet sizes are often derived as a
by-product of this process rather than from considerations of air flow. Depending on the resulting
pallet size, which will of course vary across the compass, the use of pneumatic
or electric helpers may then be required in mechanical actions to relieve the
touch. (An alternative design philosophy has been proposed by John Norman 1
in which a standard design of pallet and action is used to confer uniformity of
touch in a mechanical action organ, with the additional wind demands in the bass
being met by off-chest pneumatic servo valves. This approach will not be used
here).

It is apparent that there is still a degree of uncertainty about the best way
to design pallets. Otherwise we would not have recent mechanical action organs
which have needed electric assistance to additional pallets included apparently
as an afterthought, or those in which wind pressures are too low so that they
remain playable but otherwise ineffective, or those in which there is robbing
when all the stops are drawn. To investigate the problems some research was
done covering all aspects of the matter, but entirely from the viewpoint of wind
demand rather than the geometry of pipe plantation : firstly the wind demand of
representative pipework was addressed, then the phenomenon of robbing itself,
then the design of pallets to cope with the demand without causing robbing, and
finally methods for relieving the touch of large pallets. However the work in
the last area is not reported here as it appears elsewhere on this website 2 .
The paper addresses the major design issues in as
simple a manner as possible, and from first principles - it was assumed that a
pallet had never been designed before. Therefore existing design rules, theories,
design aids and rules of thumb are deliberately not reviewed except in one or two
instances, where they are tested against new experimental data.

There are three apertures relevant to this study through which wind must pass
in series: the first is the windway of the pallet, the second is the physical
pallet aperture (the two are not the same), and the third is the exit or load
aperture presented to the pallet by the combined pipework standing on its
groove. The key to effective design is to ensure that all of these are
explicitly addressed and stand in proper relation to each other. An added bonus
of careful design is that the pallets will not be any larger than necessary to
satisfy the wind demands of the pipes, thereby minimising pluck and hence the
need to employ touch relieving devices unless absolutely necessary.

The work described in this paper is largely experimental because modelling
gas flow through apertures, especially a sequence of apertures, is complex –
unfortunately there is no simple analogue of Ohm’s Law for electrical
circuits. This is because any concept of "resistance" due to an
aperture is not constant but varies with flow rate, pressure, aperture shape and
whether the flow is turbulent. Thus the mathematics involved at once
becomes non-linear, and only approximate theoretical solutions can generally be
derived. It is this which explains the continuing need for expensive test
facilities such as wind tunnels in aerodynamic research even with today’s
computing power. In the end, everything involving air flow has to be
derived or checked experimentally if we want to get it right, whether in
aviation, air conditioning or organs. In this study an experimental strategy was
devised which avoided the need to measure air flow rates, which is difficult
without disturbing the flow when both flows and pressures are as small as they
are in organ work.

Load aperture

If all pipes are available, regulated and voiced before a soundboard is
designed, it is not difficult to estimate the total load aperture presented to a
pallet. For each flue pipe, the smaller of foot hole area or flue area is taken
and the results added together for all pipes for a given note. (Reeds are more
difficult, but the total wind demand is usually dominated by the large flues).
This will give an approximate value for load aperture, although even this simple
process of summing areas is not generally permissible in aerodynamics 6
. However,
we have to start somewhere! In this study an attempt was made to generate a
representative generic model for the apertures of various flue ranks, but based
on experimental data. The model was used to test subsequent stages of the pallet
design process without tying the results too closely to a particular organ.

A set of measurements was first made of flue area and foot hole area for the
lowest two octaves of a great organ open diapason (8’), voiced, regulated and
installed in a respectable-sounding church organ. Although the pipework was of
no particular pedigree, it had the advantage of being in generally excellent
condition thereby facilitating accurate measurements - foot holes were nicely
circular, and flues rectangular. For each pipe the smaller of foot hole or flue
area was taken, and the values plotted graphically. The values increased sharply
towards the bottom note as would be expected, but by plotting the logarithm of
area the data fell quite close to a straight line (Figure 1). This gave some
confidence that the values could be used as the basis of a simple model for
further use.

The purely empirical equation of the straight line was:

log10y = 2.4 – 0.043n
(1)

where y is the pipe windway area (mm2), i.e. the smaller of
flue or foot hole area;

and n is the serial number of the note (n = 1 for CC)

By extrapolating the line down an octave, an estimate of windway for a 16’
diapason rank of similar scale could be obtained. As a "health check"
on the results, the area (about 745 mm2) so obtained for the CCC pipe
was examined, which could give a flue orifice some 212 mm by 3.5 mm. This might
seem rather ponderous for a manual double, but it was used for reasons to be
mentioned later. The line was also extrapolated up an octave to generate a
similar generously scaled 4’ rank.

Using these three sets of data the windways for the pipes of a hypothetical
organ with the synoptic specification 16.8.8.8.4.4 were derived. Only the lowest
two octaves were considered as it is in this region where issues of pallet
design are most important. The three 8’ stops were identical as regards
aperture, as were the two 4’ ones, even though this would be unlikely in
practice. Thus upperwork was not included (as it was relatively negligible), but
nor were reeds (which were not). The non-appearance of reeds was compensated to
some extent by the use of generous scales for the 16’ ranks and the duplicated
8’ and 4’ ones. Results are shown in Table 1.

Serial

16' rank

8' rank

8' rank

8' rank

4' rank

4' rank

Total area

bottom C

1

746

228

228

228

69

69

1568

C#

2

676

206

206

206

63

63

1420

D

3

612

187

187

187

57

57

1286

D#

4

555

169

169

169

52

52

1165

E

5

502

153

153

153

47

47

1055

F

6

455

139

139

139

42

42

956

F#

7

412

126

126

126

38

38

865

G

8

373

114

114

114

35

35

784

G#

9

338

103

103

103

31

31

710

A

10

306

93

93

93

28

28

643

A#

11

277

85

85

85

26

26

582

B

12

251

77

77

77

23

23

528

tenor C

13

228

69

69

69

21

21

478

C#

14

206

63

63

63

19

19

433

D

15

187

57

57

57

17

17

392

D#

16

169

52

52

52

16

16

355

E

17

153

47

47

47

14

14

322

F

18

139

42

42

42

13

13

291

F#

19

126

38

38

38

12

12

264

G

20

114

35

35

35

11

11

239

G#

21

103

31

31

31

10

10

216

A

22

93

28

28

28

9

9

196

A#

23

85

26

26

26

8

8

178

B

24

77

23

23

23

7

7

161

middle C

25

69

21

21

21

6

6

146

Table 1. Calculated windway areas for lowest two octaves
(all in mm2)

The right hand column is the sum of the aperture areas for each note, and it
therefore represents an estimate of the load aperture for which the pallet for
that note has to be designed. Of course, if data for the stops of a given
instrument are available then these can be inserted in the table. But it was
considered helpful to see whether a simple generic method for aperture
estimation, such as that just described, would give useful results. The data
will be re-examined at the end of the paper when they will be used as the basis
of a pallet design process. (Of incidental interest was the
observation that the values for area in Table 1 approximately halve on the 8th
note inclusive. Thus the square roots of the values halve on the 16th
note or so. The scaling constant for this diapason rank was therefore revealed
without having measured the diameter of a single pipe!).

Robbing

Robbing is the unpleasant effect caused by pipes going noticeably out of tune
when they cannot draw sufficient wind from the groove, and it is caused by the
pallet throttling the wind when many stops are drawn. It is of interest to
quantify this effect.

Accurate measurements of fundamental frequency (pitch) were made of a stopped
diapason pipe taken from an organ sounding tenor E (174.6 Hz) as the wind
pressure was varied. The measurements were made with the foot hole plugging
intact, partly because this is the usual way in which pipes are regulated and it
was considered important to use a pipe in the condition that would be found in
an organ. However a more compelling reason was that, with the plugging removed,
the wind pressures became so small that it would have been impossible to measure
them accurately. Frequency was measured to a precision of 0.1 Hz with a
microphone connected to an electronic frequency meter, and wind pressure with a
water manometer. Results are shown in Figure 2.

Between about 174 and 179 Hz the variation of frequency with pressure was
accurately linear apart from measurement errors. Below this the pipe rapidly
ceased to speak, and above it the pipe began to change to an overblowing mode in
which it eventually spoke the twelfth. Such a characteristic is qualitatively in
good agreement with the accepted theory of flue pipes 4, but it was
necessary to do this experiment to get the accurate data needed for this work.
The important point is that the pitch of a flue pipe will vary with any
change in wind pressure, but it is clearly impossible to design a practical
pallet that would not have any effect at all on pressure as the wind demand on
it was varied by drawing different numbers of stops. So the question we have to
answer is: what is the maximum amount of pitch deviation that would be
acceptable for there to be a verdict of no robbing on an instrument?

The empirical equation of the straight line was:

f = 0.0829p + 170.2
(2)

where f is fundamental frequency in Hz and p is wind pressure in mm wg.

A pitch change that can be considered tolerable would be that which
characterises a recently tuned organ, and a criterion of 0.2 Hz is suggested.
This is the same as one beat in 5 seconds between two unison ranks of notionally
the same pitch. So, using equation 2, a pitch change of 0.2 Hz would correspond
to a pressure change of 2.4 mm for this pipe. At a typical working pressure of
75 mm this implies that the pressure in the groove should not deviate by more
than about 3% when all stops are drawn.
This sounded rather a tall order, and bearing in mind that the pitches of other
ranks would also be shifting in the same direction (although not by identical
amounts), perhaps a less demanding criterion of 10% would be a more reasonable
figure to adopt for the regulation of wind pressure in the groove. For the pipe
considered this would result in a pitch change of about 0.6 Hz. The beats
resulting from such a deviation from true pitch would of course be highly
noticeable, although perhaps not positively objectionable, so the 10% figure
should be taken as an upper working limit for pressure regulation in the groove
beyond which we should not go. Desirably we should aim for less than 10%.

Pallet Design

There are two distinct apertures associated with a pallet. One is the windway
(a1) defined by the amount the pallet descends, and the other
is the physical aperture closed by the pallet when at rest (a2).
Values for the geometric areas of these apertures are given by:

a1 = d(l + w)
(3)

and

a2 = lw
(4)

where d is the pallet descent measured at the end of the aperture;

l is the length of the pallet aperture;

and w is the width of the pallet aperture.

Superficially, a2 must not be less than a1
if the pallet is not to be throttled by its own aperture. But nor must it be too
much greater if pluck is to be minimised, and this has been explored by John
Norman 3 . From geometrical considerations he showed that nothing is
gained in terms of air flow by making w > 2d, but for minimum
pluck at the key w should not exceed 1.3d. This design rule was
investigated experimentally.

A test rig was built, illustrated below, in which a large pallet was used with a physical aperture (i.e. a2
) 300mm by 18mm. However, constrictor plates could be fitted to the aperture to
reduce it to any desired degree. Pallet descent could be set to any value,
thereby varying a1, as could the wind pressure (up to a
maximum of 300mm wg). The pallet fed a rectangular exit or load aperture
situated above the groove (equivalent to the pipework fed by the pallet) whose
area was variable by means of a sliding shutter. Two manometers monitored the
input and output pressures at the pallet.

The pallet test rig

This comprises two pallets, one of which is
operated directly by means of a pull-down wire whereas the other incorporates
various methods of touch relief such as a balanced valve. The latter are not
described here but in another article on this site (see Touch
Relief in Mechanical Actions). The rig was also used for
experiments on electric actions, again not described here (see Response
Speed of Electric Actions). Wind at about 300mm (12 inches) water
gauge enters at the rear via a box fitted with an adjustable spill valve which
enables the pressure to be set and automatically maintained at the desired
level. The two water manometers referred to in the text are also at the
rear, connected by PVC tubing to the input and output of the pallet. The
sliding shutter which acts as a variable load aperture can be seen on the top of
the box. The front of the box is covered with perspex (lucite).

In the first experiment the effect of pallet aperture width (w) was
investigated. Pallet descent (d) was constant at 6mm, and the input wind
pressure was 100mm wg. Two values of w were used, 10mm and 18mm, the
former value being obtained by using a constrictor plate over the pallet
aperture. For each value of w the variation of output wind pressure from
the pallet as a function of load aperture area was measured. Results are in
Table 2.

One would of course expect to see the output pressure from the pallet falling
as the load aperture increased in size. However the centre column shows that the
rate of fall was greater for the narrower pallet aperture. Thus the narrower
pallet exerted a distinct self-throttling effect as the load aperture was
increased, compared to the right hand column which relates to a much wider
pallet aperture. This implies that even a w/d ratio of 1.7 may be too
small, thus the ratio of 1.3 suggested for minimum pluck would significantly
worsen air flow.

In a second experiment the pallet descent (d) was varied while keeping
the aperture width constant - the full width of 18mm was used throughout. Two
values of pallet descent were used (8 and 10mm), and the input wind pressure was
constant at 75mm. For each value of pallet descent the variation of output wind
pressure as a function of load aperture area was measured as before, giving the
results in Table 3. The interesting feature of these results is that, while the
windway of the pallet (a1) increased by 25% as the pallet
descent increased from 8mm to 10mm, hardly any more wind was admitted by it.
This can be seen from the centre and right hand columns - any differences
between the two were small and dominated by experimental error, thus the pallet
began to limit the delivery of air in both cases once the load aperture reached
an area of about 500 mm2. Again, therefore, the w/d ratio of
1.8 was too small.

Therefore from these two experiments it seems desirable that the ratio w/d
should exceed 1.8, particularly for pallets in which the descent d is
large, and a value of at least 2 is probably more appropriate. Pluck will
increase in proportion but this is inevitable. (Note that this conclusion is not
incompatible with John Norman’s work, which concluded that in practice pallet
aperture width could take values up to twice the pallet descent). The above
experiments were necessary to ensure that subsequent work used a pallet that was
not self-throttling, in view of the fact that robbing was to be investigated.
The central question to be answered was: what size of pallet (defined in terms
of its windway a1) is required to feed a given load aperture
whilst maintaining the pressure drop across the pallet less than 10%? (Recall
that the 10% criterion was derived from the earlier study on robbing).

A series of measurements was performed with a pallet descent of 6mm and a
generous aperture width of 18mm. Thus the pallet was unlikely to be
self-throttled by virtue of the results just discussed. As before, the output
pressure from the pallet was measured as a function of exit (load) aperture area
for a given input pressure. This was repeated for a range of input pressures
from 50 to 150 mm wg. Results are in Figure 3.

For each curve, the load aperture which caused a pressure drop across the
pallet of 10% was measured, giving the results in Table 4 .

There is evidence of a trend in the data, suggesting that the permissible
load aperture gets smaller as the wind pressure goes up (apart from the value
for 150mm pressure, which may have been unduly affected by measurement errors).
However the decrease in load aperture values is only about 30% for a 3-fold
increase in wind pressure, suggesting that we can average the load aperture
values to arrive at an approximate single figure. This turns out to be about 600
mm2 . Since the geometrical pallet windway (a1)was
about 1800 mm2 using equation (1), we can conclude that this pallet
can only feed a load aperture one third of its own windway if the pressure drop
across the pallet is to be kept below 10%. To see whether the result applied to
other values of pallet descent, a number of other measurements were made. For
example, for a descent of 8 mm (a1 = 2400 mm2 approximately)
the load aperture for a 10% pressure drop was 750 mm2 , some 31% of
the pallet windway. So, again, the factor of about one third applied in this
case.

The one-third factor is an important result for three reasons: the pallet
dimensions and its descent used for the measurements are representative of what
might be used for the lowest notes of an organ; the result was robust over a
wide range of wind pressures and various values of pallet descent; and the
easily measurable geometrical windway area a1was used rather
than vaguer parameters such as "effective aperture" or similar terms
found in other work. Finally, we should recall that the work on robbing
suggested that a pressure drop across the pallet of 10% was a working maximum
and better should aimed for. So a more cautious approach would be to use a
factor of between three and four for the aperture ratio to further reduce the
danger of robbing.

Putting it all together

We now have all the information necessary to design the pallets for the hypothetical organ represented by Table 1.
Only the lowest 19 notes are considered here for reasons mentioned later. The
following factors were used in designing the pallets:

·

In order to prevent robbing the pallet windway (a1)
was taken as 3.5 times the load aperture of the pipework (the right hand
column in Table 1).

·

The pallet aperture length (l) was a maximum of 300mm
but could be smaller.

·

The pallet aperture width (w) was at least twice the figure for
pallet descent, and somewhat more for the lowest notes.

·

Pallet descent (d) was varied across the range, implying
variable leverages in a mechanical action, but it did not exceed 10mm or
reduce below 6 mm to keep the leverages within practical limits.

·

More than one pallet was used if necessary to achieve the
desired windway value.

Results are in Table 5. This table contains all parameters necessary to
define a pallet for each note, and in addition it shows what the pluck at the
key would be (assuming a key fall of 10mm and a wind pressure of 75 mm wg).

Note

Load aperture (from Table 1)

Required pallet windway (mm2)

Pallet descent (mm)

Pallet aperture width (mm)

Pallet aperture length (mm)

No. of pallets

Key pluck at 75 mmwg (gm)

bottom C

1568

5487

10

22

300

2

495

C#

1420

4970

9

20

300

2

405

D

1286

4501

8

18

300

2

324

D#

1165

4077

7

15

300

2

236

E

1055

3693

7

15

300

2

236

F

956

3344

6

13

300

2

176

F#

865

3029

10

22

300

1

248

G

784

2744

10

20

300

1

225

G#

710

2485

9

18

300

1

182

A

643

2251

8

16

300

1

144

A#

582

2039

7

14

300

1

110

B

528

1846

7

14

300

1

110

tenor C

478

1672

6

12

300

1

81

C#

433

1515

6

12

300

1

81

D

392

1372

6

12

275

1

74

D#

355

1243

6

12

210

1

57

E

322

1125

6

12

200

1

54

F

291

1019

6

12

175

1

47

F#

264

923

6

12

160

1

43

Table 5. Pallet design figures for the load apertures in
Table 1.

Some features of interest are:

·

The pallets become progressively larger towards the
bottom note, in a manner dictated purely by the wind demand rather than
soundboard dimensions. At the
top end of the range the pallets have reduced to a size which could be
continued upwards unchanged for much of the remaining compass, hence the
reason for only listing the bottom 19 notes in the table.

· Double pallets are necessary for the lowest 6 notes to provide
sufficient wind. The two pallets for a given note are assumed to be of
identical dimensions for the sake of simplicity, but in practice each would
need to be sized for the pipework assigned to it.

·

Pluck compensation to lighten the touch would need to be
introduced at some point. In this connection it is worth reminding
ourselves of the pluck advantage of a double pallet - note the drop in pluck
between bottom F# and F. This is not because the combined pallet areas are
smaller (in fact they are 18% larger for F) but because of the more
favourable leverage conferred by the smaller descent. Thus the double
pallets could be carried up further if desired. For the same reason triple
pallets might be considered for the lowest two or three notes. The pluck
figures are of course theoretical, and in practice they might be relieved
even further in the double pallet case by arranging one pallet to open
somewhat before the other (as described by Audsley 5 ).
Methods for relieving the touch will be discussed subsequently 2.

Obviously, the numbers in Table 5 resulted from the particular set of load
apertures used as well as the pallet design process itself, and they do not
apply to any particular organ. Nevertheless the features discussed above and the sizes of the pallets themselves are not
unreasonable;
they are similar to those found in several successful mechanical action
instruments. For example electric or pneumatic helpers (e.g. balanciers) are
frequently fitted to the lowest two octaves or so, and multiple pallets may
appear in the bottom octave. This confirms in a qualitative sense that the
design process outlined in this paper is reasonable, including the generic load
apertures in Table 1 relating to a hypothetical organ.

Conclusions

An experimental study from first principles has covered the main aspects of
pallet design, including the air load presented by pipework, robbing, and the
design of pallets which should avoid robbing. The following were the main
results:

1. A simple generic model for the air load presented by flue pipes was
feasible and useful as a tool for investigating pallet design options.

2. An examination of robbing showed that the pressure drop across a
pallet should not exceed 10% of the input pressure when all stops are drawn.

3. The widths of pallet apertures should be at least twice the value of
pallet descent to prevent self-throttling and thus an extra contribution to
robbing.

4. A pallet can feed a load aperture no greater than about one third of
its geometrical windway (the area a1 in equation 3). This
is a useful practical criterion in view of the ease with which the windway
can be calculated.

5. These design factors resulted in pallet dimensions for the lowest
register of an organ which were realistic.

It is legitimate to ask whether the work described here advances or merely
confirms the state of the art of pallet design, or even whether it contributes
anything original. It is left to readers to make this judgement, but the fact
that it is based entirely on simple ab initio measurements may make it
worth having read this far. Because unsatisfactory organs (especially those with
mechanical action) can still appear, as noted in the introduction to this paper,
the degree of understanding of the subject clearly varies somewhat between
builders. Hopefully the data herein will result in some clarification of the
issues.